If $r_1$ and $r_2$ are the roots of the equation $t^2+bt+c=0$, where b and c are constants, are both $r_1$ and $r_2$ positive?

1. $b<0$
2. $c<0$

Can a circular manhole cover fit exactly into the circular recessed area of the street?

1. The recessed area of street measures 24 inches from one side to the other through its center point.
2. The area of the surface of the manhole cover is $144\pi$ inches squared.

In 2009, Marcos placed a total of $26,000 in 23 different investments. In 2010, he placed additional funds  into two new investments. For all 25 investments, is the average (arithmetic mean) amount of money per investment less than $1,200?

1. Each investment added in 2010 contained more than $1,000.
2. Each investment added in 2010 contained less than $1,500.

Women who are married sleep more soundly than women who have never married or lost a partner, according to research from an eight-year study. Furthermore, it is well established that sleeping less than six hours a night makes you 12% more likely to die prematurely than someone who sleeps up to eight hours. Therefore, getting married increases a woman's life expectancy.

Which of the following, if true, does NOT strengthen the argument above?

Archeologists have discovered ancient coins near Antioch in modern Turkey, minted by a variety of neighboring countries, that date from the time of the Roman Empire. The archaeologists have inferred that, under the rule of the Roman Empire, Antioch was transformed into a major center of trade.

Which of the following would, if true, most significantly strengthen the archeologists' inference?

Citizen: at our city's airport, we have invested time and money in security checkpoints that are a waste of time. We train and staff security staff for the purpose of searching incoming automobiles, but we search fewer than five percent of those automobiles. We might as well disband the security checkpoints. The cost is wasted, and there is a ninety-five percent chance that an illegal substance would get through the checkpoint anyway.

Council member: Even if we granted that those odds didn't justify the costs--which I disagree with--you seem not to recognize that the presence of the checkpoint itself deters some people who would bring in illegal substances from doing so.

The council member responds to the citizen's argument by

A major car company experienced a drop in sales in the month following the publication of a widely read review of the latest model, which asserted the new model was of low quality. The company also received numerous complaints from consumers who had read the review. The company, nevertheless, insists that negative reactions to the review had nothing to do with the company's subsequent drop in sales.

Which of the following, if true, most strongly supports the company's position?

Elephants are one of few animal species with intelligence and a capacity for empathy similar to that of humans. They habitually bury their dead by placing sticks and leaves over a member of their herd that has died. They are not known to bury animals other than elephants, but in some cases they have mourned humans with which they had established a relationship, leading to the theory that elephants will bury other animals with which they have had a direct relationship, but only those animals. Surprisingly, however, elephants have been found to visit the burial locations of other elephants they never knew in life.

Which of the following, if true, most helps to explain the surprising finding?

The council of Durton, which wants to avoid overly depleting the surrounding forest through exports of lumber, is considering subsidizing the import of certain kinds of wood to offset partly the deforestation. Such a step could actually put the forest in more severe danger, since insects often get into wood and can be introduced as a highly destructive force into habitats where they are non-native. Moreover, in the vast majority of cases in which a lumber-exporting city has become a lumber-importing city, the forest surrounding that city has been wiped out a few years after the switch.

The answer to which of the following would be most useful for evaluating the argument above?

Callers to a customer help line frequently complained about the quality of service. Seventy percent of survey respondents cited the services agents' lack of knowledge of how to solve the problems they were calling about. To address the problem, management decided that each service agent should go through regular training. Each agent spent half a day each week in sessions covering how to respond to callers' problems. Nevertheless, after three months of training, the rate of caller complaints has not decreased.

Which of the following, if true, most helps to explain why the training failed to achieve its goal?

In early civilizations, the development of early calendar systems—motivated most often by the desire to improve crop production—often coincided with the advancement of mathematics and astronomy. Granted, the practice of studying celestial bodies also gave rise to astrology and religion, which often had the effect of slowing the progress of the former two areas. Nevertheless, the inhibiting effect of astrology and religion is unlikely to have a lasting impact on mathematical and astronomical progress. Therefore, in all likelihood, the advancement of agrarian science, by motivating the development of measuring seasons and time, led to improved understanding of mathematics and astronomy in early civilizations.

In the argument given, the two boldfaced portions play which of the following roles?

A small company with a radical four-day work week system is considering changing its policy. Currently, this company requires all employees to arrive at work in the company's office Monday through Thursday; they need not work Friday. The proposed policy would permit each employee every week to choose one day from Monday to Friday not to work.

The adoption of this policy would be most likely to decrease employees' productivity if the employees' job functions required them to

Domestic agriculture is struggling because agriculture from overseas is available at lower prices. Since improved agrarian technology would enable domestic farmers to produce agriculture at more competitive costs, to improve the competitiveness of domestic agriculture, the government plans to subsidize domestic farmers, because as it pays subsidies directly to these domestic farmers, the farmers will have the funds they need to invest in technology.

Which of the following, if true, raises the most serious doubt regarding the effectiveness of the government's plan to improve the competitiveness of domestic agriculture?

Company A provides a business software for which companies pay an annual subscription fee, which includes help support provided by Company A's team of account managers. To reduce the cost of providing help support to half of last year's cost, Company A has redesigned its product offering to include two variants. To achieve this, Company A plans this year to move enough of its clients into a cheaper subscription that includes no access to help support to reduce the number of account managers to half of last year's number.

Which of the following is required for the redesigned product offering to achieve its aim?

Springfield's city council wants to minimize the city's average yearly expenditures on its parking meters and so is considering replacing the coin-operated meters currently in use with roadside kiosks at which parking slips can be purchased via credit card. Since many of the coin-operated meters require replacement, the costs associated with the conversion to credit card kiosks would be minimal.

Which of the following would it be most useful to know in determining whether switching to roadside kiosks would be likely to help minimize Springfield's yearly maintenance costs?

Studies indicate that potential buyers of an expensive product are more likely to go through with their purchase if they have first made a purchase of a related product, such as a less expensive product sold by the same company in the same place. Psychologists attribute this behavior to commitment bias, in which people's present actions are influenced by a desire to act consistently with their past actions. A company that sells expensive products will increase sales of these items by first inducing customers to buy less expensive, easy-to-sell items.

Which of the following, if true, most strongly supports the recommendation above?

Nationside, an insurance company, is considering issuing a new policy to insure automobile drivers who are elderly and have a record of car accidents. If premiums for the new policy are inappropriately high for a potential customer, that customer will not opt for the new policy. Therefore, Nationside is concerned that the income from the policies would not be sufficient to pay for the claims that would be made.

Which of the following strategies would be most likely to maximize Nationside's profit margins from the new policy?

Dadaism, the avant-garde European artistic movement of the early twentieth century, a phenomenon in which the postwar economic and moral sentiments gave birth to art that appeared to reject logic and embrace chaos.

An estimated three in four sea turtles fall prey to hungry birds, fish, or other perils in their first year, but those that survive have life expectancies of decades and can live over a century.